Advertisement

An Efficient Parallel Algorithm for Computing Bicompatible Elimination Ordering (BCO) of Proper Interval Graphs

  • B. S. Panda
  • Sajal K. Das
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2552)

Abstract

In this paper, we first show how a certein ordering of vertices, called bicompatible elimination ordering (BCO), of a proper interval graph (PIG) can be used to solve optimally the following problems: finding Hamiltonian cycle in a Hamiltonian PIG, the set of articulation points and bridges, and the single source or all pair shortest paths. We then propose an NC parallel algorithm (i.e., polylogarithmic-time employing a polynomial number of processors) to compute a BCO of a proper interval graph.

Keywords

Leaf Node Parallel Algorithm Hamiltonian Cycle Interval Graph Chordal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. Been, R. Fagin, D. maier, and M. Yannakakis, On the desirability of acyclic database schemes, J. ACM 30 (1983) 479–513.CrossRefGoogle Scholar
  2. [2]
    P. Buneman, A characterization of rigid circuit graphs, Discrete Mathe. 9 (1974) 205–212.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Buneman, The recovery of trees from measures of dissimilarity, in: mathematics in the Archaeological and Historical Sciences, Edinburg University Press, Edinburg (1972) 387–395.Google Scholar
  4. [4]
    R. Chandrasekharan and A. Tamir, Polylomially bounded algorithms for locating p-centers on a tree, Math. Programming 22 (1982) 304–315.CrossRefMathSciNetGoogle Scholar
  5. [5]
    R. Cole, Parallel merge sort, SIAM J. Comput. 17 (1988) 770–785.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    D.R. Fulkerson and O. S. Gross, Incidence matrices and interval graphs, Pacific J. Math. 15 (1965) 835–855.zbMATHMathSciNetGoogle Scholar
  7. [7]
    F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combin. Theory, ser B 16 (1974) 47–56.MathSciNetGoogle Scholar
  8. [8]
    M.R. Garey and D. S. Johnson, Computers and Intractability: A guide to the theory of NP-completeness, W.H. Freeman and Company (1979).Google Scholar
  9. [9]
    M. C. Golumbic, Algorithmic graph theory and perfect graphs, Academic press, New York. (1980)zbMATHGoogle Scholar
  10. [10]
    Chin-wen Ho and R.C.T. Lee, Counting clique trees and computing perfect elimination schemes in parallel, IPL 31 (1989) 61–68.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    R. E. Jamison and R. Laskar, Elimination orderings of chordal graphs, in “Proc. of the seminar on Combinatorics and applications,” ( K. S. Vijain and N. M. Singhi eds. 1982) ISI, Calcutta, pp. 192–200.Google Scholar
  12. [12]
    P. N. Klein, Efficient parallel algorithms for chordal graphs, SIAM J. Comput. 25 (1996) 797–827.zbMATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    C. L. Monma and V. K. Wei, Intersection graphs of paths in a tree, J. Combin. Theory, Ser. B 41 (1986) 141–181.CrossRefMathSciNetGoogle Scholar
  14. [14]
    C. Papadimitriou and M. Yannakakis, Scheduling interval ordered tasks, SIAM J. Comput. 8 (1979) 405–409.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    F. S. Roberts, Indifferences graphs, in:“Proof Techniques in Graph Theory”, (F. Harary ed.) 1971, pp.139–146, Academic Press.Google Scholar
  16. [16]
    D. Rose, A graph theoretic study of the numerical solution of sparse positive definite systems of linear equations: in R. Read ed, Graph Theory and Computing ( Academic Press, New York, 1972) 183–217.Google Scholar
  17. [17]
    J.R. Walter, representation of chordal graphs as subtrees of a tree, J. Graph Theory 2 (1978) 265–267.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • B. S. Panda
    • 1
  • Sajal K. Das
    • 2
  1. 1.Department of MathematicsIndian Institute of Technology, DelhiNew DelhiIndia
  2. 2.Department of Computer Science and EngineeringThe University of Texas at ArlingtonArlingtonUSA

Personalised recommendations